A recent report compiled by A. DECOVILLE published by the Ecole Nationale des Telecommunications, 46 rue Barrault, Paris, Report no. 90 SIG 005, 1990, showed that as far as the industrial production of reverberators is concerned, special effects generators, without particular reference to the acoustics of a room or to the auditory perception of the space, can be distinguished from reverberator systems proper which are aimed at convincingly reproducing the acoustics of one or a type of room and whose adjustment parameters are related to the physical characteristics of enclosed sites.
As far as reverberators proper are concerned, the response to an impulse sound excitation of an auditorium shows that, as is represented in FIG. 1a, the typical echogram comprises the direct sound followed by the first echoes or temporally early echoes which can be registered by the ear, then finally a continuum perceived on the contrary as a sound trail. This sound trail, termed late reverberation, is characteristic of the auditorium itself, since it is, to a first approximation, independent of the relative positions and of the spread of the sources and listeners, this not being the case for the first echoes.
Conventionally, since a realistic simulation of the space effect must encompass the first echoes and the late reverberation, a reverberator usually includes, as is represented in FIGS. 1b, a FIR filter (finite impulse response digital filter) 102 simulating the first echoes, and a reverberant filter 104, formed by a recursive network of digital delays and capable of reproducing the characteristic properties of the late reverberation. The reverberator shown in FIG. 16 also includes amplifiers 106, 108, 110 and adder 112.
More precisely, the elementary basic structures of the majority of commercial reverberators consist in the use of filters, so-called comb filters and all-pass filters. These filters are widely known in the state of the art. The comb filter has a disadvantage, in the frequency domain, arising from the periodicities of its spectral response causing a colouration perceived as a metallic timbre. The same is true for the all-pass filter when the input signal is not stationary, as in the case of speech signals and music.
The two aforesaid filters have furthermore the disadvantage, in the time domain, of exhibiting a low density of echoes of their impulse response, thus engendering the phenomenon known as flutter in the transients.
So as to eliminate the colouration phenomenon and increase the density of echoes, M. R. SCHROEDER proposed using in cascade a parallel association of comb filters, termed a comb sum, and a series association of all-pass filters, as is represented in FIGS. 1c, compare the publication "Natural sounding artificial reverberation", J. Audio.Eng.Soc. 10(3):219-223, 1962. For a comb filter, the reverberation time Tr is given by the relation: ##EQU2## where, for a cell of rank i, gi designates the loop gain of rank i, mi the duration of delays, expressed as an integer number of sampling periods T.
For a comb sum, the assigning to each comb of the same reverberation time Tr entails a choice of the loop gain gi related to the duration of the delay mi.
Such a choice implies that, for each cell of rank i, .gamma.=gi.sup.1/mi, .gamma. designating the corresponding modulus of the poles.
Compare the publication by J.M.JOT and A.CHAIGNE "Digital delay networks for designing artificial reverberators", Proc. 90th A.E.S. Convention, Paris 1991, preprint 3030(E-2) hereafter designated [JOT, CHAIGNE, 91]. The interpretation of the aforesaid conditions, so that no particular mode is audible during the late reverberation, which would correspond to an undesired colouration, is therefore that all the resonant modes of the reverberant filter must possess the same attenuation time constant. For N comb filters in parallel, the modal density, the number of resonant modes per Hz, can be written: ##EQU3## .tau.i being the duration of the delay of the cell of rank i in seconds, and the echo density compare [JOT, CHAIGNE, 91] ##EQU4##
For sufficiently similar durations .tau.i, the number N of comb filters can be written: ##EQU5##
In order to retain a reasonable number N of elementary cells M. R. SCHROEDER proposed associating a series all-pass filter in cascade with the comb sum. The all-pass filter enables the density of echoes to be increased without noticeably modifying the timbre of the reverberation, defined by the comb filters associated in parallel.
Although such a solution makes it possible to determine, overall, the reverberation time, it does not enable the resonances of the all-pass filters to be taken into account. Further, no study has made it possible to show how to avoid the defects of sonority of the series all-pass filter and to determine the number of all-pass cells, their delay or loop gain values in order to obtain a given density of echoes. Thus, the choice of the parameters of the all-pass filters remains essentially empirical.
In actual auditoria, the physical phenomena of sound absorption mean that the damping of the sound waves depends on frequency. The reverberator such as represented in FIGS. 1c formed the subject of an adaptation by the replacing of each loop gain gi by an IIR, infinite impulse response filter, low-pass filter, so as to simulate the absorption of sound in air. Compare J. A. MOORER "About this reverberation business", Computer Music Journal 3(2):13-18, 1979.
Such a method makes it possible neither to take into account the absorption of sound by the walls of the room, the absorption due to air usually being negligible, neither to control, in calculating the coefficients of the filters, the variation in reverberation time as a function of frequency. This technique also entails the interdependence of the adjustments in the reverberation time and the energy of the reverberated signal as a function of frequency. This problem is unsolved for the comb sum structure of FIGS. 1c.
Another approach making it possible to multiply the number of echoes in the response of the reverberant filter, the multi-channel approach, has been proposed. The latter, consisting in appending loopback channels linking the various delays, makes it possible progressively to increase the density of echoes in the impulse response, as in the case of actual rooms.
STAUTNER and PUCKETTE, in the article "Designing multi-channel reverberators", Computer Music Journal 6(1), 1982, have proposed the structure represented in FIGS. 1d. These authors, limiting themselves to studying the stability of the aforesaid structure, propose however a particular 4-channel embodiment using a loopback transfer matrix of the form ##EQU6##
In this embodiment, the echo density is not a maximum, by reason of the nullity of some transfer coefficients of delay elements 3i, and the use of the gain parameter g of multiplier elements 15i alone to control the reverberation time amounts to assigning an identical attenuation to every delay, without taking their durations into account. Furthermore, just as in the case of the comb sum filter, corresponding to the case where the matrix A is diagonal, this choice involves the risk that all the resonant modes do not have an identical decay time, thus not guaranteeing the absence of colouration of the transients.
More recently, a general model, such as represented in FIGS. 1e, has been proposed, compare [JOT, CHAIGNE, 91 ]. This model essentially comprises a reference filter consisting in fact of a reverberant filter all of whose poles have unit modulus, an infinite reverberation time thus being obtained at every frequency. Such a situation obtains if the loopback matrix 120 is a unit matrix when the delays are free of attenuation. The main subject of the previously cited article [JOT, CHAIGNE, 91 ] is the study of the conditions for obtaining the aforesaid constraints in respect of the reference filter, the introduction of attenuations having been envisaged, in this article, at the very most for the purpose of controlling the reverberation time of comb filters.